1 Pay 20 to play this game A spin the following spinner win

1. Pay $20 to play this game. A spin the following spinner, win $75 if the pointer is in the area showing $75 win nothing otherwise.

(Pie Chart with .25 of the pie chart for the winning area)

A. Develop a probability distribution

B. Find the expected value

C. Find the variance and the standard deviation

D. Does the game favor the player or the organizer of the game?

E. What is the fair price to play this game?

Solution

P(w) = 0.25

P(l) = 0.75

Probability of winning r times out of x times = (0.25)^r * (0.75)^(x-r)

b.

Expected value:

P(w) = 0.25

W = 75 - 20 = 55 $

P(l) = 0.75

L = -20 $

E(x) = W * P(w) + (-L) * P(l)

E(x) = 0.75 * 55 - 20 * 0.75

E(x) = -1.25 $

Expecting 1.25$ loss on an average.

c.

V = p*(1-p) = 0.25 * 0.75 = 0.1875

S.d =sqrt(V) = sqrt ( 0.1875) = 0.433

d.

As expected value is -1.25$, this game is favor to organizers.

e.

lets say x is amount to be paid for playing,

W = 75 - x

L = -x

P(w) = 0.25

P(l) = 0.75

for fair game,

E(x) =0

E(x)=0 = w*P(w) + L*P(l)

0.25*(75-x) = x * 0.75

75-x = 3x

x = 75/4

x = 18.75$

so fair price is 18.75$